bezier_curves.h

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#ifndef BEZIER_CURVES_H
#define BEZIER_CURVES_H
 
#include <vector>
#include <math/vector2d.h>
 
template <typename T> class ELLIPSE;
 
class BEZIER_POLY
{
public:
    BEZIER_POLY( const VECTOR2I& aStart, const VECTOR2I& aCtrl1,
                 const VECTOR2I& aCtrl2, const VECTOR2I& aEnd );
 
    BEZIER_POLY( const std::vector<VECTOR2I>& aControlPoints );
 
    BEZIER_POLY( const std::vector<VECTOR2D>& aControlPoints )
        : m_ctrlPts( aControlPoints )
    {
        m_minSegLen = 0.0;
    }
 
    void GetPoly( std::vector<VECTOR2I>& aOutput, int aMaxError = 10 );
    void GetPoly( std::vector<VECTOR2D>& aOutput, double aMaxError = 10.0 );
 
private:
 
    void getQuadPoly( std::vector<VECTOR2D>& aOutput, double aMaxError );
    void getCubicPoly( std::vector<VECTOR2D>& aOutput, double aMaxError );
 
    int findInflectionPoints( double& aT1, double& aT2 );
    int numberOfInflectionPoints();
 
    double thirdControlPointDeviation();
 
    void subdivide( double aT, BEZIER_POLY& aLeft, BEZIER_POLY& aRight );
    void recursiveSegmentation( std::vector<VECTOR2D>& aOutput, double aMaxError );
 
    void cubicParabolicApprox( std::vector<VECTOR2D>& aOutput, double aMaxError );
 
    bool isNaN() const;
 
    bool isFlat( double aMaxError ) const;
 
    VECTOR2D eval( double t );
 
    double m_minSegLen;
 
    std::vector<VECTOR2D> m_ctrlPts;
};
 
 
// TODO: Refactor BEZIER_POLY to use BEZIER
 
template <typename NumericType>
class BEZIER
{
public:
    BEZIER() = default;
 
    constexpr BEZIER( const VECTOR2<NumericType>& aStart, const VECTOR2<NumericType>& aC1,
                      const VECTOR2<NumericType>& aC2, const VECTOR2<NumericType>& aEnd ) :
            Start( aStart ), C1( aC1 ), C2( aC2 ), End( aEnd )
    {
    }
 
    constexpr VECTOR2<NumericType> PointAt( double aT ) const
    {
        const double t2 = aT * aT;
        const double t3 = t2 * aT;
        const double t_m1 = 1.0 - aT;
        const double t_m1_2 = t_m1 * t_m1;
        const double t_m1_3 = t_m1_2 * t_m1;
 
        return ( t_m1_3 * Start ) + ( 3.0 * aT * t_m1_2 * C1 ) + ( 3.0 * t2 * t_m1 * C2 )
               + ( t3 * End );
    }
 
    VECTOR2<NumericType> Start;
    VECTOR2<NumericType> C1;
    VECTOR2<NumericType> C2;
    VECTOR2<NumericType> End;
};
 
template<typename T>
void TransformEllipseToBeziers( const ELLIPSE<T>& aEllipse, std::vector<BEZIER<T>>& aBeziers );
 
#endif  // BEZIER_CURVES_H